Allegra Versace, the 20-year-old daughter of the designer Donatella and the heir to the fashion house, is suffering from anorexia, her mother has disclosed. She released a joint statement with Allegra's father, Paul Beck, in an attempt to quash speculation.

"Our daughter, Allegra, has been battling anorexia, a very serious disease, for many years," the statement, issued on Tuesday, said. "She is receiving the best medical care possible to help overcome this illness and is responding well."

The disclosure comes at a time when the fashion industry is wrestling with the effects of the illness and the example it sets through its use of very thin models. Several fashion houses have said they will not use overly thin models to advertise their clothes, and fashion shows in several countries have moved to prevent so-called size zero models from appearing on their catwalks.

Allegra Versace was left 50% of the fashion house following the murder of her uncle, Gianni, the founder of the company, in Miami in 1997. She came into her inheritance, worth $150m (£76.4m), when she turned 18, and is currently studying fashion in New York. The rest of the company is split between Donatella and her brother, Santos.

The attempt to put an end to the rumours about Allegra's condition, however, served to heighten speculation. Some reports said that Allegra, pictured above in 2005, was "consumed" by the illness and had been hospitalised. The company denied the reports.

"Due to numerous media reports, we want to let everyone know that we appreciate their concern for Allegra, and we ask that her privacy be respected at this time," her parents said.